Big Idea:
There's theory and then there's what actually happens.

I'll begin by asking the essential question: What is the difference between theoretical probability and experimental probability?

Here I will provide examples of experimental probability used in everyday life. The most common ones that I can think of come in sports. Like I may ask, who does a basketball coach put in the game to shoot a free throw for a technical foul? Those familiar with basketball will know it's the best free throw shooter based on his or her free throw percentage. That percentage is an example of experimental probability.

We will complete the definitions and then I'll present the examples.

For each example we will compare the experimental probability to the theoretical probability by converting the ratio to a decimal. I'll provide calculators for this work. I don't want to have kids spend a lot of time dividing 12 by 35!

Be careful to annotate the examples because students may confuse the number 4 on the spinner with the number of trials or some either incorrect value.

A similar check for understanding problem is provided with the example.

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This set of problems can be solved by students in pairs or groups. I have chosen to limit all of the probabilities to simple events for this lesson. Perhaps a extension could involve compound probabilities. The main reason for this is that the lesson was written for in a transition to the common core year. The state standards for 7th grade ask students to find experimental probabilities of simple events. I thought it would be best to focus on that.

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Students will work on the next set of problems independently. These problems are similar in structure to the problems from the previous practice set. The first problem ask students to explain the difference between experimental and theoretical probability. They may word this however they choose, but I hope their answer conveys that the theoretical probability is what we expect to happen and the experimental probability is what actually happens. If time permits, we will run simulations to show that over many trials (hundreds, thousands, millions,etc) experimental probability begins to approach theoretical probability. This simulations are easy to set up using a random number generator in excel.

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The exit ticket has three parts. Students should identify the theoretical probability of an event, the experimental probability for that same event, and then explain the difference in meaning of the two types of probability.

I will probably score this out of 4 points. This first two parts are worth 1 point each. The third part will be worth two points if there is a valid explanation in a complete sentence.

Big Idea:
students complete classwork in pairs and reflect on the difference between theoretical and experimental probabilities, including why they do not always equal each other when an experiment is carried out